Giant uniaxial negative thermal expansion in FeZr2 alloy over a wide temperature range

Negative thermal expansion (NTE) alloys possess great practical merit as thermal offsets for positive thermal expansion due to its metallic properties. However, achieving a large NTE with a wide temperature range remains a great challenge. Herein, a metallic framework-like material FeZr2 is found to exhibit a giant uniaxial (1D) NTE with a wide temperature range (93-1078 K, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\alpha }}_{l}=-34.01\times {10}^{-6}\,{{{{{{\rm{K}}}}}}}^{-1}$$\end{document}α¯l=−34.01×10−6K−1). Such uniaxial NTE is the strongest in all metal-based NTE materials. The direct experimental evidence and DFT calculations reveal that the origin of giant NTE is the couple with phonons, flexible framework-like structure, and soft bonds. Interestingly, the present metallic FeZr2 excites giant 1D NTE mainly driven by high-frequency optical branches. It is unlike the NTE in traditional framework materials, which are generally dominated by low energy acoustic branches. In the present study, a giant uniaxial NTE alloy is reported, and the complex mechanism has been revealed. It is of great significance for understanding the nature of thermal expansion and guiding the regulation of thermal expansion.


Thermal expansion behavior and detailed structural information for the MZr2 (M = Fe, Ni) systems
In order to provide insights into the mechanism of FeZr2 with giant uniaxial (1D) NTE over a wide temperature range, here, we comparatively studied the isostructural MZr2 systems. It can be found that there is a vastly different in the anisotropic thermal expansion between the two materials ( Fig. S2 and Fig. S6).  the CTE ofαl-X = 30.59 ± 0.02 × 10 -6 K -1 andαl-Y = 29.26 ± 0.02 × 10 -6 K -1 in the RD-X and RD-Y directions between 107 to 500K, respectively. As a contrast, the average CTE for lattice parameter a is αa = 25.75 ± 0.04 ×10 -6 K -1 for FeZr2 between 10 to 500K (αa = 29.75 ± 0.04 × 10 -6 K -1 , 100K-500K) extracted from the NPD (Fig. S6a). These result in the planar thermal expansion of the ingot showing nearly the same CTE as the a-axis. Since FeZr2 is tetragonal crystal symmetry. And the EBSD indicates that its grain orientations of [001] and [110] are random distribution inside the RD-RD plane. As previously reported, the sample cooling process will produce a strong texture due to large temperature gradients. 1 For example, a giant anisotropic magnetocaloric effect can be achieved by the arc melting method. 1 The targeted sample FeZr2 was prepared by arc melting in the copper crucibles under a high-purity argon atmosphere.

The linear thermal expansion of MZr2
The upper surface is heated by the electric arc. And the bottom of the sample is in contact with the copper crucible, which results in an extreme temperature difference between the top and bottom surfaces of the sample. It will produce a vast temperature gradient between the upper and bottom surfaces of the sample. This results in FeZr2 ingots with a strong texture.

The SXRD, NPD results of MZr2, and nPDF for FeZr2
The SXRD patterns of MZr2 measured at room temperature (RT) could refine well using a single I4/mcm structure by the Rietveld refinement method (Fig. S3), indicating that both components are pure phase and possess the same crystal structure. Except for the crystal structure diffraction peak, no new magnetic or diffraction peak mutation was found at the NPD measurement for all components ( Fig. S3 and S8    Both different ranges of r at a large interval (2~50 Å) or short interval (2~10 Å) at different temperatures can be well fitted with the same structure (I4/mcm) model by pdfgui (Fig. S5), indicating the average and local structures of FeZr2 are consistent.
Furthermore, the structure of FeZr2 has good structural stability in the measurement temperature range.
Corresponding to the c-axis NTE, the a-axis transitions from a large PTE to a normal PTE (Fig. S6a). Fig. S6c shows the variable temperature axial ratios (c/a), discovering that FeZr2 has a large c/a than NiZr2. Interestingly, the difference in the atomic radius of Fe compared to that of Ni is negligible 4 . Still, the lattice parameter c of FeZr2 is much larger than NiZr2 at room temperature (Table S1). It indicates, with increasing temperature, the rapidly decreasing c/a of FeZr2 indicates that a large c/a is necessary to produce a large 1D NTE.
Moreover, the two materials exhibit vastly different anisotropic thermal expansion, but the intrinsic volumetric thermal expansion of FeZr2 and NiZr2 is a little different ( Fig. S6d), and the αV is 17.73 ± 0.07 × 10 -6 K -1 and 24.60 ± 0.04 × 10 -6 K -1 between 10K to 500K corresponding to FeZr2 and NiZr2, respectively.   are randomly distributed in the RD-RD plane.   It can be found that the vibration directions of Zr atoms in FeZr2 prefer transverse vibrations for the Zr-Zr bonds (Fig. 12b,c,d). It is due to the Zr-Zr bonds (distances less than 3.2Å) having relatively strong interactions (Table S7), which make the Zr-Zr bonds more inclined to bend rather than stretch. It can be found that there are no changes in the variable temperature K-edge XANES spectra change for all the elements (Fig. S13), indicating that 1D NTE due to electron transfer is excluded.

FeZr2 NiZr2
Zr   all cross the Fermi level, as shown in Fig. S20(d). However, in these five d-orbitals, we find that M-dz 2 is changing the largest. From Fe to Ni, we demonstrate the quick decrease of a peak above the Fermi level comes from dz 2 -orbital.